### Examining the Ratio: The Importance of Running the Ball for the Philadelphia Eagles

#### by Jerome's Friend

Eagles Defensive Coordinator Billy Davis’ father, Bill Davis, served as the Eagles’ linebackers coach under Dick Vermeil and also coached the special teams in 1977 and 1978. After Bill transitioned to Cleveland, first as Director, then as Vice President of Player Personnel, he returned to Philadelphia in 1988 when Eagles President Harry Gamble hired him to be the team’s Vice President of Player Personnel. Bill was charged with helping head coach Buddy Ryan evaluate and bring in more talented players. When Bill Davis resigned after the 1989 season, Buddy offered the position to Ted Plumb, his offensive coordinator for four years (Plumb didn’t take it). Along with the fans, Buddy had grown tired of Plumb’s ineffective play calling and wanted to move in a more exciting direction (unfortunately, that direction was Rich Kotite). Under Plumb, the Eagles offense had become predictable. Series after maddening series, Plumb routinely called runs on first down, runs on second, and passes on third. It’s interesting then, to contrast that era with the fatigue surrounding Andy Reid’s pass-first philosophy. As Chip Kelly and Harry Gamble’s son, Tom, continue to weigh pros and cons for potential starting quarterbacks, a lot of emphasis has been placed recently on the Eagles passing game. But perhaps this should be an echo of the past and not represent what may be most important. Instead, it might be beneficial to re-examine, or quantify, how significant running the ball is for this football team.

Since the NFL is so clearly cyclical, both in playing trends (and now, evidently, with coaching and front office legacies), how important is a balanced attack for today’s Philadelphia Eagles? In the last three years, Andy Reid’s teams have had a pass/run ratio of 1.3 to 1. In the team’s 22 wins, that ratio dropped to 1.1 to 1, and in the team’s 26 losses the ratio increased 1.6 to 1. This seems to indicate that yes, a more balanced attack leads to more wins. However, in seven of those 26 losses, the Eagles had a balanced attack (a ratio of 1.3 to 1 or below), and in eight of the team’s 22 wins, they did not (a ratio greater than 1.3 to 1). This indicates that averages don’t tell the whole story. If we wish to examine whether a lower pass/run ratio, or rather, a higher run/pass ratio, truly results in more wins, we can perform a logistic regression.

Logistic regression can be used when we want to see the strength and significance between some independent variable and a dependent, dichotomous outcome. In other words, we want to see how the run/pass ratio for each Eagles game in the past three years related to wins and losses. If results are statistically significant, the logistic regression model will produce a p-value less than .001. If results are strong, a statistic called an odds ratio, which in this case will represent the ratio of winning odds to losing odds, will be high. After entering the run/pass ratios and win/loss data from the last three years into a logistic regression function, here are the primary results (detail here – Eagles Run Ratio – Logistic Regression):

Since the p-value is less than .001, the results are statistically significant. This is substantial because it means the high odds ratio (38.1306) is meaningful. In effect, the results of the logistic regression model tell us that there is indeed a strong, significant relationship between the run/pass ratio and wins and losses. As the run/pass ratio increases, or the more often the Eagles run the ball, the more likely they are to win a football game. In fact, every time the run/pass ratio increases by one unit, the Eagles are 38 times more likely to win a football game. For example, on October 9, 2011 in Buffalo, the Eagles rushed 20 times and passed 40, resulting in a .50 run/pass ratio. According to this logistic regression model, that ratio gives the Eagles a 22.44% chance of winning (they lost 31-24). But on December 18, 2011 against the New York Jets, the Eagles rushed 33 times and passed 22, a 1.5 run/pass ratio and a one unit increase over the .50 ratio from the Buffalo game. In this model, a 1.5 run/pass ratio gives the Eagles a 91.7% chance of winning (they beat New York 45-19), and means that the Eagles were 38 times more likely to win with that higher run/pass ratio against New York than with the run/pass ratio against Buffalo (click on the file above for win probabilities for each of the Eagles 48 games).

In an NFL where passing and quarterback play are held in higher regard, these results are counter-intuitive. They indicate that, for our Eagles, running the ball more often will result in more victories. But these results must be taken with a grain of salt. The regression does not control for increased rushing attempts when protecting a lead, or increased passing attempts when playing from behind. However, these phenomena may offset each other. Also, this is a historical analysis with a relatively small sample size. And since Andy Reid is no longer the head coach, these results may not project to Chip Kelly’s team. But the NFL is also cyclical. For example, if history is any indication, the 2013 Billy Davis/Tom Gamble tandem will bode well (During Bill Davis and Harry Gamble’s first year together, the Eagles drafted Keith Jackson and Eric Allen). It’s also exciting to consider that, for a head coach with a fondness for science, these results may foretell the next trend in Eagles football. And it just so happens we have one of the best running backs in the league currently on the roster.

**Updated 3/2/2013 to include comment regarding game context. *

*You can follow Philly’s Inferno on Facebook and Twitter (@JeromesFriend). Jerome’s Friend is not a mathematician, just an Eagles fan.*

I was never worried about the ratio of runs/passes as that can be misleading in a game. I was always more aggravated by the timing of the runs and passes, and the fact that Reid rarely tried to win a game via the run, even when saddled with poor receivers.

Yeah, great point. I wonder if there was some way to incorporate timing into this. Probably not… it may be too subjective. I agree with you though.

Is there any way to delete the fourth quarter from your analysis? My intuition is that run totals are inflated in games where the team has the lead and therefore “milks” the clock in the fourth. Perhaps looking at only the first three quarters will better show whether running the ball contributed to winning?

Just had this discussion on Twitter. I was a little lazy in this regard, and justified it by thinking that pass totals can be inflated when the team is coming from behind, so the two may cancel each other out.

Although quarterly totals aren’t a part of my dataset, I should be able to remove the 4th quarter results with some more digging. Maybe this weekend, if time permits.

to use an well-used phrase, “correlation is not causality”. You should use more careful wording than “As the run/pass ratio increases, or the more often the Eagles run the ball, the more likely they are to win a football game.”

You could also just as easily state, “the more likely the Eagles are to win a football game, the more they will run the ball.” It’s not very scientific if you can’t distinguish the causal direction.

Very true. Great comment.

Jerome you should really this but with half time splits because while your ran/pass ratio in the first half might be 1.5, but if you suddenly are behind by 2 TDs, you will come out in the 2nd and pass away and the ratio will drop and that will scew the results its also true the other way around if you start out by passing alot, gets in front and then protects the lead and end up with a very good run/pass ratio.

This very old FO article debunks the myth http://www.footballoutsiders.com/stat-analysis/2003/establishment-clause

As well. In general teams there run alot in the 4th quarter wins more games

[…] when playing from behind are phenomena that do not offset each other. Therefore the basis for my earlier conclusion that running more often may lead to more Eagles victories is not necessarily true. But after further research and analysis, it’s not entirely wrong […]

Can someone find out if the Eagles threw the ball more often then the Patriots during the Tom Brady/Andy Reid Eras? I have been complaining that the team with the better QB (Brady) ran the ball more than the team with the better RB’s (Westbrook & McCoy). That stat alone should help prove what fans have been complaining about for years. And I do think the ratio will be better with Chip Kelly, but I do think we still will throw the ball slightly more than we run. Hopefully 51% – 52% to 49% – 48%.